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Realizability algebras III: some examples

Published online by Cambridge University Press:  03 May 2016

JEAN-LOUIS KRIVINE
JEAN-LOUIS KRIVINE*
Affiliation:
University Paris-Diderot - C.N.R.S., France Email: jean-louis.krivine@pps.univ-paris-diderot.fr
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Abstract

We use the technique of “classical realizability” to build new models of ZF + DC in which R is not well ordered. This gives new relative consistency results, which are not obtainable by forcing. This gives also a new method to get programs from proofs of arithmetical formulas with dependent choice.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Issue 1 , January 2018 , pp. 45 - 76
Copyright
Copyright © Cambridge University Press 2016 

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